W7 review

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 26 Nov 2009 09:27:42 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/26/t1259252944djz8zhgtzc5ewpu.htm/, Retrieved Thu, 26 Nov 2009 17:29:16 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Nov/26/t1259252944djz8zhgtzc5ewpu.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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No (this computation is public)

User-defined keywords:

W7 review

Dataseries X:

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2.3 2.0 1.9 2.3 2.7 0 2.8 2.3 2.0 1.9 2.3 0 2.4 2.8 2.3 2.0 1.9 0 2.3 2.4 2.8 2.3 2.0 0 2.7 2.3 2.4 2.8 2.3 0 2.7 2.7 2.3 2.4 2.8 0 2.9 2.7 2.7 2.3 2.4 0 3.0 2.9 2.7 2.7 2.3 0 2.2 3.0 2.9 2.7 2.7 0 2.3 2.2 3.0 2.9 2.7 0 2.8 2.3 2.2 3.0 2.9 0 2.8 2.8 2.3 2.2 3.0 0 2.8 2.8 2.8 2.3 2.2 0 2.2 2.8 2.8 2.8 2.3 0 2.6 2.2 2.8 2.8 2.8 0 2.8 2.6 2.2 2.8 2.8 0 2.5 2.8 2.6 2.2 2.8 0 2.4 2.5 2.8 2.6 2.2 0 2.3 2.4 2.5 2.8 2.6 0 1.9 2.3 2.4 2.5 2.8 0 1.7 1.9 2.3 2.4 2.5 0 2.0 1.7 1.9 2.3 2.4 0 2.1 2.0 1.7 1.9 2.3 0 1.7 2.1 2.0 1.7 1.9 0 1.8 1.7 2.1 2.0 1.7 0 1.8 1.8 1.7 2.1 2.0 0 1.8 1.8 1.8 1.7 2.1 0 1.3 1.8 1.8 1.8 1.7 0 1.3 1.3 1.8 1.8 1.8 0 1.3 1.3 1.3 1.8 1.8 0 1.2 1.3 1.3 1.3 1.8 1 1.4 1.2 1.3 1.3 1.3 1 2.2 1.4 1.2 1.3 1.3 1 2.9 2.2 1.4 1.2 1.3 1 3.1 2.9 2.2 1.4 1.2 1 3.5 3.1 2.9 2.2 1.4 1 3.6 3.5 3.1 2.9 2.2 1 4.4 3.6 3.5 3.1 2.9 1 4.1 4.4 3.6 3.5 3.1 1 5.1 4.1 4.4 3.6 3.5 1 5.8 5.1 4.1 4.4 3.6 1 5.9 5.8 5.1 4.1 4.4 1 5.4 5.9 5.8 5.1 4.1 1 5.5 5.4 5.9 5.8 5.1 1 4.8 5.5 5.4 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Inflatie[t] = + 0.543937208204278 + 1.03190587642702`yt-1`[t] + 0.00311594207492439`yt-2`[t] + 0.0625948070164088`yt-3`[t] -0.223419091554451`yt-4`[t] + 0.55477286988978Kredietcrisis[t] + 0.138013235580985M1[t] -0.0633444684359386M2[t] + 0.0412969737820374M3[t] + 0.0160581190123575M4[t] + 0.118222226316890M5[t] -0.0266887211638146M6[t] + 0.120851047017496M7[t] -0.0360998595273063M8[t] -0.136471275857123M9[t] -0.00225950808331554M10[t] + 0.193711021693291M11[t] -0.0192085947006778t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 0.543937208204278 0.38108 1.4274 0.161644 0.080822 `yt-1` 1.03190587642702 0.160828 6.4162 0 0 `yt-2` 0.00311594207492439 0.242829 0.0128 0.989829 0.494915 `yt-3` 0.0625948070164088 0.256666 0.2439 0.808638 0.404319 `yt-4` -0.223419091554451 0.17637 -1.2668 0.21295 0.106475 Kredietcrisis 0.55477286988978 0.334214 1.6599 0.105159 0.052579 M1 0.138013235580985 0.368967 0.3741 0.710444 0.355222 M2 -0.0633444684359386 0.368265 -0.172 0.864344 0.432172 M3 0.0412969737820374 0.370395 0.1115 0.911811 0.455906 M4 0.0160581190123575 0.371267 0.0433 0.965727 0.482863 M5 0.118222226316890 0.368993 0.3204 0.750427 0.375213 M6 -0.0266887211638146 0.370597 -0.072 0.942967 0.471484 M7 0.120851047017496 0.373598 0.3235 0.748106 0.374053 M8 -0.0360998595273063 0.371068 -0.0973 0.92301 0.461505 M9 -0.136471275857123 0.388445 -0.3513 0.727283 0.363642 M10 -0.00225950808331554 0.390185 -0.0058 0.99541 0.497705 M11 0.193711021693291 0.38966 0.4971 0.621963 0.310981 t -0.0192085947006778 0.010719 -1.792 0.081101 0.040551 Multiple Linear Regression - Regression Statistics Multiple R 0.95872572457677 R-squared 0.919155014965253 Adjusted R-squared 0.882987521660234 F-TEST (value) 25.4138435089642 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 1.11022302462516e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.545063925154349 Sum Squared Residuals 11.2895979351773 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.3 2.27321040082170 0.0267895991782954 2 2.8 2.42685717305492 0.373142826945083 3 2.4 3.12480485873162 -0.724804858731624 4 2.3 2.6655895626774 -0.365589562677398 5 2.7 2.60837978685045 0.09162021314955 6 2.7 2.71996353244859 -0.0199635324485925 7 2.9 2.93264923867934 -0.0326492386793361 8 3 3.01025074468127 -0.0102507446812690 9 2.2 2.90511687308668 -0.705116873086679 10 2.3 2.20742590062897 0.0925740993710305 11 2.8 2.44646133207841 0.353538667921589 12 2.8 2.67738849333687 0.122611506663128 13 2.8 2.98274585919984 -0.182745859199843 14 2.2 2.771135054835 -0.571135054835001 15 2.6 2.12571483071886 0.474285169281138 16 2.8 2.49216016657436 0.307839833425642 17 2.5 2.74518634708374 -0.245186347083740 18 2.4 2.43120760812847 -0.0312076081284717 19 2.3 2.37856473612543 -0.0785647361254265 20 1.9 2.03544079261394 -0.135440792613939 21 1.7 1.56355308356984 0.136446916430161 22 2 1.4870111329814 0.5129888670186 23 2.1 1.97002562891933 0.129974371080669 24 1.7 1.93808005800904 -0.23808005800904 25 1.8 1.70789620294184 0.0921037970581553 26 1.8 1.52850786827228 0.271492131727719 27 1.8 1.56687247803506 0.233127521964937 28 1.3 1.61805214588813 -0.318052145888126 29 1.3 1.16271281112303 0.137287188876974 30 1.3 0.997035297904183 0.302964702095818 31 1.2 1.64884193776639 -0.448841937766391 32 1.4 1.48120139465543 -0.0812013946554349 33 2.2 1.56769096470285 0.632309035297149 34 2.9 2.50258254663094 0.397417453369059 35 3.1 3.43903221942445 -0.339032219424449 36 3.5 3.44006696507057 0.0599330349294315 37 3.6 3.83733823660459 -0.237338236604593 38 4.4 3.57733449967483 0.82266550032517 39 4.1 4.46895774703691 -0.36895774703691 40 5.1 4.03432313237825 1.06567686762175 41 5.8 5.17598367524432 0.624016324755676 42 5.9 5.5398004732883 0.360199526711704 43 5.4 5.90312392834682 -0.503123928346822 44 5.5 5.03172035645236 0.468279643547639 45 4.8 4.86363907864063 -0.0636390786406308 46 3.2 4.20298041975869 -1.00298041975869 47 2.7 2.84448081957781 -0.144480819577808 48 2.1 2.04446448358352 0.0555355164164808 49 1.9 1.59880930043201 0.301190699567986 50 0.6 1.49616540416297 -0.896165404162971 51 0.7 0.313650085477540 0.386349914522460 52 -0.2 0.489874992481871 -0.689874992481871 53 -1 -0.392262620301541 -0.607737379698459 54 -1.7 -1.08800691176954 -0.611993088230457 55 -0.7 -1.76317984091798 1.06317984091798 56 -1 -0.758613288403004 -0.241386711596996 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.386476754207049 0.772953508414097 0.613523245792951 22 0.236467953194860 0.472935906389721 0.76353204680514 23 0.128308737649625 0.25661747529925 0.871691262350375 24 0.0707207791659167 0.141441558331833 0.929279220834083 25 0.0320473324343146 0.0640946648686291 0.967952667565685 26 0.0132101221697683 0.0264202443395366 0.986789877830232 27 0.00493330502319232 0.00986661004638463 0.995066694976808 28 0.00275314053678324 0.00550628107356649 0.997246859463217 29 0.000950251194011456 0.00190050238802291 0.999049748805989 30 0.000283634394580252 0.000567268789160503 0.99971636560542 31 0.000198447690583984 0.000396895381167968 0.999801552309416 32 0.000944130285586264 0.00188826057117253 0.999055869714414 33 0.0115541614491485 0.0231083228982970 0.988445838550851 34 0.00570277473159127 0.0114055494631825 0.994297225268409 35 0.00424616509520294 0.00849233019040588 0.995753834904797 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.466666666666667 NOK 5% type I error level 10 0.666666666666667 NOK 10% type I error level 11 0.733333333333333 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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